Integrable deformations of T-dual $\sigma$ models

Abstract

We present a method to deform (generically non-abelian) T duals of two-dimensional $\sigma$ models, which preserves classical integrability. The deformed models are identified by a linear operator $\omega$ on the dualised subalgebra, which satisfies the 2-cocycle condition. We prove that the so-called homogeneous Yang-Baxter deformations are equivalent, via a field redefinition, to our deformed models when $\omega$ is invertible. We explain the details for deformations of T duals of Principal Chiral Models, and present the corresponding generalisation to the case of supercoset models.

5 pages. References added. Projector reinstated in eq. (3). Claims on DTD with degenerate cocycle corrected

References in corpus (9)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Integrable Deformations of Strings on Symmetric Spaces
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices

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